Large time behaviour of the solution of a parabolic-hyperbolic system modelling the codiffusion of isotopes

We study the asymptotic behaviour of the solution of a hyperbolic-parabolic problem in an isolated domain when $t \to \infty$. The problem models the diffusion of $n$ species of radiative isotopes of the same element in a medium. The model is based on the assumption that, since the isotopes are chemically indistinguishable, the flux of each isotope depends on the gradient of the total concentration of the element weighted by the relative percentage of the isotope. We show that the asymptotic behaviour strongly depends on the radiative law, and, in some cases, on the pointwise distribution of the initial concentration.